• Journal of the korean Society of Automotive Engineers
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• v.15 no.2
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• pp.92-104
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• 1993

In the present study, the velocity profiles and entrance length of developing transitional pulsating flows are investigated both analytically and experimentally in the entrance region of a square duct. The systems of conservation equations for transitional pulsating flows in a square duct are solved analytically by linearizing the non-linear convective terms. Analytical solutions are obtained in the form of infinite series for velocity pofiles. The experimental study for the air flow in a square duct(40mm*40mm*4000mm) is carried out to measure velocity profiles and other parameters by using a hot-wire anemometer with a data acquisition and processing system. The distribution of velocity profiles( $u_{ps}$ / $u_{m,ta}$) in the decelerating period is higher than in the accelerating period. The distribution of the axial component of the axial component of velocity in the transitional flow is nearly uniform in the central region of the duct, and decrease rapidly near the wall. The entrance length correlation of the transitional pulsating flows in a square duct is obtained to be $L_{e}$/ $D_{h}$=0.83 $A_{1}$R $e_{ta}$ /(.omega. sup+1)$^{2}$TEX>

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.9 no.4
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• pp.561-571
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• 1997

In this paper, the fundamental equations are developed for the pulsatile laminar flow generated by changing the oscillatory flow with $0{\leq}f{\leq}48Hz$ into a steady one with $0{\leq}Re{\leq}2500$ in a rigid circular pipe. Analytical solutions for the wave propagation factor k, the axial distributions of cross-sectional mean velocity $u_m$ and pressure p are schematically derived and confirmed experimentally. The axial distributions of centerline velocity and pressure were measured by using Pitot-static tubes and strain gauge type pressure transducers, respectively. The cross-sectional mean velocity was calculated from the centerline velocity by applying the parabolic distribution of the laminar flow and it was confirmed by using the ultrasonic flowmeter. It was found that the axial distributions of cross-sectional mean velocity and pressure agree well with theoretical ones and depend only on the Reynolds number Re and angular velocity $\omega$.

• Nuclear Engineering and Technology
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• v.53 no.7
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• pp.2084-2094
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• 2021

Delta-form-based methods for solving high order spatial discretization schemes are introduced into the reactor S_N transport equation. Due to the nature of the delta-form, the final numerical accuracy only depends on the residuals on the right side of the discrete equations and have nothing to do with the parts on the left side. Therefore, various high order spatial discretization methods can be easily adopted for only the transport term on the right side of the discrete equations. Then the simplest step or other robust schemes can be adopted to discretize the increment on the left hand side to ensure the good iterative convergence. The delta-form framework makes the sweeping and iterative strategies of various high order spatial discretization methods be completely the same with those of the traditional S_N codes, only by adding the residuals into the source terms. In this paper, the flux limiter method and weighted essentially non-oscillatory scheme are used for the verification purpose to only show the advantages of the introduction of delta-form-based solving methods and other high order spatial discretization methods can be also easily extended to solve the S_N transport equations. Numerical solutions indicate the correctness and effectiveness of delta-form-based solving method.

• Ocean Systems Engineering
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• v.12 no.3
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• pp.359-384
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• 2022

We develop in this work a new well-balanced preserving-positivity path-conservative central-upwind scheme for Saint-Venant-Exner (SVE) model. The SVE system (SVEs) under some considerations, is a nonconservative hyperbolic system of nonlinear partial differential equations. This model is widely used in coastal engineering to simulate the interaction of fluid flow with sediment beds. It is well known that SVEs requires a robust treatment of nonconservative terms. Some efficient numerical schemes have been proposed to overcome the difficulties related to these terms. However, the main drawbacks of these schemes are what follows: (i) Lack of robustness, (ii) Generation of non-physical diffusions, (iii) Presence of instabilities within numerical solutions. This collection of drawbacks weakens the efficiency of most numerical methods proposed in the literature. To overcome these drawbacks a reformulation of the central-upwind scheme for SVEs (CU-SVEs for short) in a path-conservative version is presented in this work. We first develop a finite-volume method of the first order and then extend it to the second order via the averaging essentially non oscillatory (AENO) framework. Our numerical approach is shown to be well-balanced positivity-preserving and shock-capturing. The resulting scheme could be seen as a predictor-corrector method. The accuracy and robustness of the proposed scheme are assessed through a carefully selected suite of tests.

• Journal of Pharmaceutical Investigation
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• v.29 no.4
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• pp.295-307
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• 1999

Using a Rheometries Fluids Spectrometer (RFS II), the dynamic viscoelastic properties of aqueous poly(ethylene oxide) (PEO) solutions in small amplitude oscillatory shear flow fields have been measured over a wide range of angular frequencies. The angular frequency dependence of the storage and loss moduli at various molecular weights and concentrations was reported in detail, and the result was interpreted using the concept of a Deborah number De. In addition, the experimentally determined critical angular frequency at which the storage and loss moduli become equivalent was compared with the calculated characteristic time (or its inverse value), and their physical significance in analyzing the dynamic viscoelastic behavior was discussed. Finally, the relationship between steady shear flow and dynamic viscoelstic properties was examined by evaluating the applicability of some proposed models that describe the correlations between steady flow viscosity and dynamic viscosity, dynamic fluidity, and complex viscosity. Main results obtained from this study can be summarized as follows: (1) At lower angular frequencies where De<1, the loss modulus is larger than the storage modulus. However, such a relation between the two moduli is reversed at higher angular frequencies where De>l, indicating that the elastic behavior becomes dominant to the viscous behavior at frequency range higher than a critical angular frequency. (2) A critical angular frequency is decreased as an increase in concentration and/or molecular weight. Both the viscous and elastic properties show a stronger dependence on the molecular weight than on the concentration. (3) A characteristic time is increased with increasing concentration and/or molecular weight. The power-law relationship holds between the inverse value of a characteristic time and a critical angular frequency. (4) Among the previously proposed models, the Cox-Merz rule implying the equivalence between the steady flow viscosity and the magnitude of the complex viscosity has the best validity. The Osaki relation can be regarded to some extent as a suitable model. However, the DeWitt, Pao and HusebyBlyler models are not applicable to describe the correlations between steady shear flow and dynamic viscoelastic properties.

• The Korean Journal of Rheology
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• v.10 no.4
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• pp.234-246
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• 1998

The objective of this study is to investigate the correlation between steady shear flow (nonlinear behavior) and dynamic viscoelastic (linear behavior) properties for concentrated polymer solutions. Using both an Advanced Rheometic Expansion System(ARES) and a Rheometics Fluids Spectrometer (RFS II), the steady shear flow viscosity and the dynamic viscoelastic properties of concentrated poly(ethylene oxide)(PEO), polyisobutylene(PIB), and polyacrylamide(PAAm) solutions have been measured over a wide range of shear rates and angular frequencies. The validity of some previously proposed relationships was compared with experimentally measured data. In addition, the effect of solution concentration on the applicability of the Cox-Merz rule was examined by comparing the steady flow viscosity and the magnitude of the complex viscosity Finally, the applicability of the Cox-Merz rule was theoretically discussed by introducing a nonlinear strain measure. Main results obtained from this study can be summarized as follows : (1) Among the previously proposed relationships dealt with in this study, the Cox-Merz rule implying the equivalence between the steady flow viscosity and the magnitude of the complex viscosity has the best validity. (2) For polymer solutions with relatively lower concentration, the steady flow viscosity is higher than the complex viscosity. However, such a relation between the two viscosities is reversed for highly concentrated polymer solutions. (3) A nonlinear strain measure is decreased with increasing stran magnitude, after reaching the maximum value in small strain range. This behavior is different from the theoretical prediction demonstrating the shape of a damped oscillatory function. (4) The applicability of the Cox-Merz rule is influenced by the $\beta$ value, which indicates the slope of a nonlinear stain measure (namely, the degree of nonlinearity) at large shear deformations. The Cox-Merz rule shows better applicability as the $\beta$ value becomes smaller.

• Journal of Korea Water Resources Association
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• v.44 no.6
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• pp.429-438
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• 2011

In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (RANS) equations are closed with the ${\kappa}-{\epsilon}$ model. The artificial compressibility (AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes (INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the flux-difference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.2
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• pp.179-185
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• 2016

In this paper numerical stability of CSS and ISS schemes in axisymmetric fluid-structure-burning simulation for solid rocket motors are studied. The implemented CSS and ISS algorithms for two-dimensional axisymmetric FSI problems are used to analyze ACM and BCM solid rocket motors. Numerical results from CSS and ISS schemes are compared to investigate the efficacy of ISS scheme over CSS scheme in stabilizing the numerical solution. The ACM and BCM simulation results show that ISS scheme gives stable and converged numerical solutions with appropriately small system time step size, while CSS scheme fails to converge after generating rapidly amplified oscillatory solutions. It is concluded that ISS scheme can be useful in improving the numerical stability of FSI analysis for ACM and BCM solid rocket motor simulations, which is not successfully obtained with CSS scheme.

• Korean Journal of Food Science and Technology
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• v.27 no.5
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• pp.799-806
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• 1995

The steady shear and small amplitude oscillatory dynamic rheological properties of citrus pectin $([\eta]=3.75\;dL/g)$ were characterized for a wide range of pectin concentrations $({\sim}6%)$. The typical power-law flow was observed above 2.0% concentration, and the shear rate dependence of viscosity increased with pectin concentration. The transition from dilute to concentrated regime, determined from the double logarithmic plot of ${\eta_{sp.o}}\;vs\;C[\eta]$, occurred at a critical coil overlap parameter $C^{*}[\eta]\approx4.0$, at which ${\eta_{sp.o}}$ corresponded to approximately 10.0. The slopes of ${\eta_{sp.o}}\;vs\;C[\eta]$, at $C[\eta]\;at\;C[\eta]C^{*}[\eta]$were 1.1 and 4.5, respectively. The steady viscosity $(\eta)$ displayed a good superposition at ${\eta}/{\eta}_o\;vs\;{\gamma}/{\gamma}_{0.8}$ relation with an exception of high concentration (6%), which arised from the significant deviation of flow behavior index (n values of $\eta_{a}=K\gamma^{n-1}$) at high concentration. Dynamic measurements showed that the loss modulus $(G^{\prime\prime})$ was much higher than the storage modulus $(G^\prime)$for all concentrations studied, indicating predominant viscoelastic liquid-like behavior of pectin solutions. The frequency dependence of $G^\prime$ was higher than that of $G^\prime\prime$ at the same concentration, whose trend was more pronounced with decreasing pectin concentration. The shear viscosity $(\eta)$ was almost identical to the complex viscosity $(\eta^{*})$ at low concentration, following the Cox-Merz rule, but they became increasingly different at high concentration.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.335-341
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• 2017

In this paper, beam finite elements with higher-order derivatives' continuity are formulated and evaluated for various boundary conditions. All the beam elements are based on Euler-Bernoulli beam theory. These higher-order beam elements are often required to analyze structures by using newly developed higher-order beam theories and/or non-classical beam theories based on nonlocal elasticity. It is however rare to assess the performance of such elements in terms of boundary and loading conditions. To this end, two higher-order beam elements are formulated, in which $C^2$ and $C^3$ continuities of the deflection are enforced, respectively. Three different boundary conditions are then applied to solve beam structures, such as cantilever, simply-support and clamped-hinge conditions. In addition to conventional Euler-Bernoulli beam boundary conditions, the effect of higher-order boundary conditions is investigated. Depending on the boundary conditions, the oscillatory behavior of deflections is observed. Especially the geometric boundary conditions are problematic, which trigger unstable solutions when higher-order deflections are prescribed. It is expected that the results obtained herein serve as a guideline for higher-order derivatives' continuous finite elements.